Question

A hydraulic press has a small piston of diameter 2.8 cm. If a force of 65N is applied to a smaller piston, a force of 3 500N is exerted on the large piston. What is the diameter of the larger piston?

Answer 1

Answer:

The larger piston has a radius of 10.24cm

Explanation:

As we know that the pressure at both the ends of the large and small piston is equal therefore we can write,

∴$P_{1} = P_{2}$

We have P = $\frac{Force}{Area}$

∴The given quantities in the question are as follows:

$F_{1} = 65N$, $F_{2} = 3500N$

$D_{1} = 2.8cm$  $r_{1} = 1.4cm$

$D_{2} = ?$

Area = π$r^{2}$

65N / $A_{1}$= 3500/ $A_{2}$

$\frac{A_{2} }{A_{1} }$= $\frac{3500N}{65N}$

π$r_{2} ^{2}$ / π$(1.4)^{2}$= 700/ 13

$r_{2}$ = 10.24 cm

Therefore the radius of the larger piston is 10.24cm.